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Annual Review of Statistics and Its Application

Volume 8, 2021

Quantile Regression for Survival Data

Abstract

Quantile regression offers a useful alternative strategy for analyzing survival data. Compared with traditional survival analysis methods, quantile regression allows for comprehensive and flexible evaluations of covariate effects on a survival outcome of interest while providing simple physical interpretations on the time scale. Moreover, many quantile regression methods enjoy easy and stable computation. These appealing features make quantile regression a valuable practical tool for delivering in-depth analyses of survival data. This article provides a review of a comprehensive set of statistical methods for performing quantile regression with different types of survival data. The review covers various survival scenarios, including randomly censored data, data subject to left truncation or censoring, competing risks and semicompeting risks data, and recurrent events data. Two real-world examples are presented to illustrate the utility of quantile regression for practical survival data analyses.

Keyword(s): competing risks data, estimating equation, quantile regression, randomly censored data, recurrent events data, semicompeting risks data
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/content/journals/10.1146/annurev-statistics-042720-020233
2021-03-07
2024-04-27
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Literature Cited

  1. Andersen PK, Gill RD. 1982. Cox's regression model for counting processes: a large sample study. Ann. Stat. 10:1100–20
     [Google Scholar]
  2. Beran R. 1981. Nonparametric regression with randomly censored survival data Tech. Rep., Univ. Calif Berkeley:
  3. Buchinsky M, Hahn J. 1998. A alternative estimator for censored quantile regression. Econometrica 66:653–71
     [Google Scholar]
  4. Buckley J, James I. 1979. Linear regression with censored data. Biometrika 66:429–36
     [Google Scholar]
  5. Chernozhukov V, Hong H. 2001. Three-step censored quantile regression and extramarital affairs. J. Am. Stat. Assoc. 97:872–82
     [Google Scholar]
  6. Clayton D. 1978. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. 65141–51
  7. Cox DR. 1972. Regression models and life-tables. J. R. Stat. Soc. Ser. B 34:187–202
     [Google Scholar]
  8. Cummings F, Gray R, Tormey D, Davis T, Volk H et al. 1993. Adjuvant tamoxifen versus placebo in elderly women with node-positive breast cancer: long-term follow-up and causes of death. J. Clin. Oncol. 11:29–35
     [Google Scholar]
  9. De Backer M, El Ghouch A, Van Keilegom I 2017. Semiparametric copula quantile regression for complete or censored data. Electron. J. Stat. 11:1660–98
     [Google Scholar]
  10. De Backer M, El Ghouch A, Van Keilegom I 2019. An adapted loss function for censored quantile regression. J. Am. Stat. Assoc. 114:1126–37
     [Google Scholar]
  11. De Backer M, El Ghouch A, Van Keilegom I 2020. Linear censored quantile regression: a novel minimum-distance approach. Scand. J. Stat. 47:1275–306
     [Google Scholar]
  12. Efron B. 1967. The two-sample problem with censored data. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4 LM Le Cam, J Neyman 831–53 Berkeley: Univ. Calif. Press
     [Google Scholar]
  13. Fine JP, Jiang H, Chappell R 2001. On semi-competing risks data. Biometrika 88:907–19
     [Google Scholar]
  14. Fitzenberger B. 1997. A guide to censored quantile regressions. Handb. Stat. 15:405–37
     [Google Scholar]
  15. Fygenson M, Ritov Y. 1994. Monotone estimating equations for censored data. Ann. Stat. 22:732–46
     [Google Scholar]
  16. Genest C. 1987. Frank's family of bivariate distributions. Biometrika 74:549–55
     [Google Scholar]
  17. Huang Y. 2002. Calibration regression of censored lifetime medical cost. J. Am. Stat. Assoc. 98:318–27
     [Google Scholar]
  18. Huang Y. 2010. Quantile calculus and censored regression. Ann. Stat. 38:1607–37
     [Google Scholar]
  19. Huang Y, Peng L. 2009. Accelerated recurrence time models. Scand. J. Stat. 36:636–48
     [Google Scholar]
  20. Ji S, Peng L, Cheng Y, Lai H 2012. Quantile regression for doubly censored data. Biometrics 68:101–12
     [Google Scholar]
  21. Ji S, Peng L, Li R, Lynn MJ 2014. Analysis of dependently censored data based on quantile regression. Stat. Sin. 24:1411–32
     [Google Scholar]
  22. Kalbfleisch JD, Prentice RL. 2002. The Statistical Analysis of Failure Time Data New York: Wiley. , 2nd. ed.
  23. Koenker R. 2005. Quantile Regression Cambridge, UK: Cambridge Univ. Press
  24. Koenker R. 2008. Censored quantile regression redux. J. Stat. Softw. http://dx.doi.org/10.18637/jss.v027.i06
    [Crossref] [Google Scholar]
  25. Koenker R. 2017. Quantile regression: 40 years on. Annu. Rev. Econ. 9:155–76
     [Google Scholar]
  26. Koenker R, Bassett G. 1978. Regression quantiles. Econometrica 46:33–50
     [Google Scholar]
  27. Koenker R, Portnoy S, Ng PT, Melly B, Zeilis A et al. 2020. quantreg: quantile regression. R package version 5.74. https://cran.r-project.org/web/packages/quantreg/index.html
    [Google Scholar]
  28. Kutner NG, Clow PW, Zhang R, Aviles X 2002. Association of fish intake and survival in a cohort of incident dialysis patients. Am. J. Kidney Dis. 39:1018–24
     [Google Scholar]
  29. Li KC, Wang JL, Chen CH 1999. Dimension reduction for censored regression data. Ann. Stat. 27:1–23
     [Google Scholar]
  30. Li R, Peng L. 2011. Quantile regression for left-truncated semi-competing risks data. Biometrics 67:701–10
     [Google Scholar]
  31. Li R, Peng L. 2015. Quantile regression adjusting for dependent censoring from semicompeting risks. J. R. Stat. Soc. Ser. B 77:107–30
     [Google Scholar]
  32. Luo X, Huang CY, Wang L 2013. Quantile regression for recurrent gap time data. Biometrics 69:375–85
     [Google Scholar]
  33. Ma H, Peng L, Huang C-Y, Fu H 2020. Heterogeneous individual risk modelling of recurrent events. Biometrika In press. https://doi.org/10.1093/biomet/asaa053
    [Crossref] [Google Scholar]
  34. Miller RG. 1976. Least squares regression with censored data. Biometrika 63:449–64
     [Google Scholar]
  35. Nelson W. 2003. Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications Philadelphia: SIAM
  36. Neocleous T, Vanden Branden K, Portnoy S 2006. Correction to Censored Regression Quantiles by S. Portnoy, 98 (2003), 1001–1012. J. Am. Stat. Assoc 101:860–61
     [Google Scholar]
  37. Parzen MI, Wei LJ, Ying Z 1994. A resampling method based on pivotal estimating functions. Biometrika 81:341–50
     [Google Scholar]
  38. Peng L. 2012. A note on self-consistent estimation of censored regression quantiles. J. Multivar. Anal. 105:368–379
     [Google Scholar]
  39. Peng L, Fine J. 2009. Competing risks quantile regression. J. Am. Stat. Assoc. 104:1440–53
     [Google Scholar]
  40. Peng L, Huang Y. 2008. Survival analysis with quantile regression models. J. Am. Stat. Assoc. 103:637–49
     [Google Scholar]
  41. Portnoy S. 2003. Censored regression quantiles. J. Am. Stat. Assoc. 98:1001–12
     [Google Scholar]
  42. Portnoy S, Lin G. 2010. Asymptotics for censored regression quantiles. J. Nonparametric Stat. 22:115–30
     [Google Scholar]
  43. Powell J. 1984. Least absolute deviations estimation for the censored regression model. J. Econom. 25:303–25
     [Google Scholar]
  44. Powell J. 1986. Censored regression quantiles. J. Econom. 32:143–55
     [Google Scholar]
  45. Prentice RL. 1978. Linear rank tests with right censored data. Biometrika 65:167–79
     [Google Scholar]
  46. Reid N. 1994. A conversation with Sir David Cox. Stat. Sci. 9:439–55
     [Google Scholar]
  47. Ritov Y. 1990. Estimation in a linear regression model with censored data. Ann. Stat. 18:303–28
     [Google Scholar]
  48. Robins J, Rotnitzky A. 1992. Recovery of information and adjustment for dependent censoring using surrogate markers. AIDS Epidemiology—Methodological Issues N Jewell, K Dietz, V Farewell 24–33 Boston: Birkhauser
     [Google Scholar]
  49. Stefanski L, Carroll R. 1987. Conditional scores and optimal scores for generalized linear measurement-error models. Biometrika 74:703–16
     [Google Scholar]
  50. Sun X, Peng L, Huang Y, Lai HJ 2016. Generalizing quantile regression for counting processes with applications to recurrent events. J. Am. Stat. Assoc. 111:145–56
     [Google Scholar]
  51. Sun Y, Wang HJ, Gilbert J 2012. Quantile regression for competing risks data with missing cause of failure. Stat. Sin. 22:703–28
     [Google Scholar]
  52. Tanner MA, Wong WH. 1987. The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82:528–40
     [Google Scholar]
  53. Tsiatis A. 1975. A nonidentifiability aspect of the problem of competing risks. PNAS 72:20–22
     [Google Scholar]
  54. Tsiatis AA. 1990. Estimating regression parameters using linear rank tests for censored data. Ann. Stat. 18:354–72
     [Google Scholar]
  55. Wang H, Wang L. 2009. Locally weighted censored quantile regression. J. Am. Stat. Assoc. 104:1117–28
     [Google Scholar]
  56. Wang MC, Qin J, Chiang CT 2001. Analyzing recurrent event data with informative censoring. J. Am. Stat. Assoc. 96:1057–65
     [Google Scholar]
  57. Wei LJ, Gail MH. 1983. Nonparametric estimation for a scale-change with censored observations. J. Am. Stat. Assoc. 78:382–88
     [Google Scholar]
  58. Wei LJ, Ying Z, Lin D 1990. Linear regression analysis of censored survival data based on rank tests. Biometrika 77:845–51
     [Google Scholar]
  59. Wu Y, Yin G. 2013. Cure rate quantile regression for censored data with a survival fraction. J. Am. Stat. Assoc. 108:1517–31
     [Google Scholar]
  60. Wu Y, Yin G. 2017a. Cure rate quantile regression accommodating both finite and infinite survival times. Can. J. Stat. 45:29–43
     [Google Scholar]
  61. Wu Y, Yin G. 2017b. Multiple imputation for cure rate quantile regression with censored data. Biometrics 73:94–103
     [Google Scholar]
  62. Xia Y, Zhang D, Xu J 2010. Dimension reduction and semiparametric estimation of survival models. J. Am. Stat. Assoc. 105:278–90
     [Google Scholar]
  63. Yang X, Narisetty NN, He X 2018. A new approach to censored quantile regression estimation. J. Comput. Graph. Stat. 27:417–25
     [Google Scholar]
  64. Ying Z, Jung SH, Wei LJ 1995. Survival analysis with median regression models. J. Am. Stat. Assoc. 90:178–84
     [Google Scholar]
  65. Zhou L. 2006. A simple censored median regression estimator. Stat. Sin. 16:1043–58
     [Google Scholar]
/content/journals/10.1146/annurev-statistics-042720-020233
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Quantile Regression for Survival Data
Annual Review of Statistics and Its Application 8, 413 (2021); https://doi.org/10.1146/annurev-statistics-042720-020233
/content/journals/10.1146/annurev-statistics-042720-020233
/content/journals/10.1146/annurev-statistics-042720-020233
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  • Article Type: Review Article

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